It sounds like the battery was allowed to deep-discharge, which is generally unrecoverable. You'll have to find a new battery for it.

I do hope that is incorrect ... that a fully discharged battery breaks the
the player. If that is the case, then I have a "broken player". Let it
play until the battery indicator showed red, turned it off. A few hours
later turned it back on, and it only showed the "low battery graphic"
and would turn off. Now, connected by USB, all it shows is the
"low battery graphic" and is clearly not charging (even after 32 hours.)

My old Rio Riot did not do that.

So I toasted a brand new player because I ran the player down to
"red indicator" in the battery icon and did not immediately recharge it?

It sure acts like it is toast, while the player clearly knows it is on the USB
cable (the "low battery graphic" comes on when I connect it) it
is not negotiating with the USB host adapter nor is it charging
(has not gotten warm at all.)

It sure acts like it is toast, while the player clearly knows it is on the USB
cable (the "low battery graphic" comes on when I connect it) it
is not negotiating with the USB host adapter nor is it charging
(has not gotten warm at all.)

No, no, no, I meant that the battery was toast - though it would still require sending in the player if you're still under warranty.

As far as what's going on with the USB - the USB port doesn't provide a whole lot of power; it could be that between that and the player trying to charge a dead battery, there isn't enough power left to actually boot up the unit.

If your player is working fine, I don't recommend taking it apart. Li-Ion batts, when cared properly, can last for 2+ years giving good playback time. By the time it starts giving a short playback time, you'll probably want to replace your player with a newer one.